基于广义灰数的双向投影灰靶决策模型拓展研究
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摘要
针对属性值为广义灰数时已有灰靶决策方法的不足问题,提出了广义灰数灰靶决策方法,首先,通过定义广义灰数,将区间灰数的概念进行了进一步的拓展;其次,基于范数概念提出了广义灰数的Husdorff距离测度、算法及其性质并定义了属性值为广义灰数的靶心和靶心距概念,构建了基于正负靶心的双向投影一致性系数的广义灰数灰靶决策模型排序方法.该模型解决了属性值包含更多不确定因素的决策问题,最后通过实例验证该方法的科学合理性性和优越性.
In view of the shortcomings of the grey target decision method when the attribute value is the general grey number, the grey target decision method of general grey number is proposed. Firstly, the concept of interval grey number is further expanded by defining the general grey number. Secondly, the Husdorff distance measure, algorithm and its properties are proposed based on the concept of norm. The concept of the bull's-eye and the bull's-eye-distance of the scheme is defined. The sorting method of grey target decision model based on the bidirectional projection consistency coefficient of positive and negative bull's-eye is constructed. The model solves the problem of decision scheme with more uncertain factors.Finally, the feasibility and superiority of this method are verified by an example.
In view of the shortcomings of the grey target decision method when the attribute value is the general grey number, the grey target decision method of general grey number is proposed. Firstly, the concept of interval grey number is further expanded by defining the general grey number. Secondly, the Husdorff distance measure, algorithm and its properties are proposed based on the concept of norm. The concept of the bull's-eye and the bull's-eye-distance of the scheme is defined. The sorting method of grey target decision model based on the bidirectional projection consistency coefficient of positive and negative bull's-eye is constructed. The model solves the problem of decision scheme with more uncertain factors.Finally, the feasibility and superiority of this method are verified by an example.
引文
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[7]郭三党,方志耕.基于后悔理论的多目标灰靶决策方法[J].控制与决策,2015, 30(9):1635-1640.Guo S D, Fang Z G. Multi-object grey target decision model based on regret theory[J]. Control and Decision,2015, 30(9):1635-1640.
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[12]王正新,党耀国,杨虎.改进的多目标灰靶决策方法[J].系统工程与电子技术,2011, 31(11):2634-2636.Wang Z X, Dang Y G, Yang H. Improvements on decision method of grey target[J]. Systems Engineering and Electronics, 2011, 31(11):2634-2636.
[13]罗党.灰色多指标风险型决策方法研究[J].系统工程与电子技术,2004, 26(8):1057-1059.Luo D. Research on grey multi-criteria risk decision-making method[J]. Systems Engineering and Electronics,2004, 26(8):1057-1059.
[14]王大澳,菅利荣,刘思峰,等.基于Choquet积分的多属性灰靶群决策方法[J].控制与决策,2017, 32(7):1286-1292.Wang D A, Jian L R, Liu S F, et al. Approach for multi-attribute grey target group decision-making based on Choquet integral[J]. Control and Decision, 2017, 32(7):1286-1292.
[15]马金山.指标及权重均为混合数据类型的广义灰靶决策方法[J].统计与决策,2018(7):58-61.Ma J S. A generalized grey target decision method with mixed data type of index and weight[J]. Statistics and Decision, 2018(7):58-61.
[16]朱建军,张丽丽,梁艳华.基于冲突主体不确定证据融合的灰靶决策方法[J].控制与决策,2012, 27(7):1037-1041.Zhu J J, Zhang L L, Liang Y H. Grey target decision method based on uncertain evidence aggregation under conflict interest participants[J]. Control and Decision, 2012, 27(7):1037-1041.
[17]梁艳华.基于去键鼠的多时点多属性灰靶决策模型[J]·控制与决策,2012, 37(10):1527-1531.Liang Y H. Multi-perio and multi-criteria decision making model of grey target based on interval number[J].Control and Decision, 2012, 37(10):1527-1531.
[18]戴文战,李久亮.灰数多属性偏离靶心度群决策方法[J].系统工程理论与实践,2014, 34(3):787-792.Dai W Z, Li J L. Off-target deviation degree method grey multi-attribute group decision-making[J]. Systems Engineering—Theory&Practice, 2014, 34(3):787-792.
[19] Liu S F, Fang Z G, Yang Y J, et al. General grey numbers and their operations[J]. Grey Systems:Theory and Application, 2012, 2(3):341-349.
[20] Jiang S Q, Liu S F, Liu Z X, et al. Study on distance measuring and sorting method of general grey number[J].Grey System:Theory and Application, 2017, 6(3):319-328.
[2]刘思峰,杨英杰,吴利丰,等.灰色系统理论及其应用[M].北京:科学出版社,2014:256-258.Liu S F, Yang Y J, Wu L F, et al. Grey system theory and its application[M]. Beijing:Science Press, 2014:256-258.
[3] Yue Z L. Approach to group decision making based on determining the weights of experts by using projection method[J]. Applied Mathematical Modelling, 2012, 36(7):2900-2910.
[4] Feng J Y,Zhang H. Grey target model appraising firm's financial status based on Altman coefficients[J]. The Journal of Grey System, 2002, 5(3):274-276.
[5]宋捷,王正新,张可.正负靶心灰靶决策模型[J].系统工程理论与实践,2010, 30(10):1822-1827.Song J, Wang Z X, Zhang K. New decision model of grey target with both the positive clout and negative clout[J].Systems Engineering—Theory&Practice, 2010, 30(10):1822-1827.
[6] Ma J S. Grey target decision method for a variable target centre based on the decision maker's preferences[J]. Journal of Applied Mathematics, Volume 2014, Article ID 572529, 6 pages. http://dx.doi.org/10.1155/2014/572529.
[7]郭三党,方志耕.基于后悔理论的多目标灰靶决策方法[J].控制与决策,2015, 30(9):1635-1640.Guo S D, Fang Z G. Multi-object grey target decision model based on regret theory[J]. Control and Decision,2015, 30(9):1635-1640.
[8]闫书丽,刘思峰,吴利丰.一种基于前景理论的三参数区间灰数型群体灰耙决策方法[J].控制与决策,2015, 30(1):105-108.Yan S L, Liu S F, Wu L F. Agroup grey target decision making method with three parameter interval greynumber based on prospect theory[J]. Control and Decision, 2015, 30(1):105-108.
[9] Huang Y S, Chang W C, Li W H. Aggregation of utility-based individual preferences for group decision-making[J].European of Operational Research, 2013, 229(2):462-469.
[10] Liu S F, Yang Y J, Forrest J. Grey data analysis methods:Models and applications[M]. Springer-Verlag, 2016:230-234.
[11]党耀国.基于区间数的多指标灰靶决策模型的研究[J].中国工程科学,2005, 7(8):33-35.Dang Y G. Study on the multi-attribute decision model of grey target based on interval number[J]. Engineering Science, 2005, 7(8):33-35.
[12]王正新,党耀国,杨虎.改进的多目标灰靶决策方法[J].系统工程与电子技术,2011, 31(11):2634-2636.Wang Z X, Dang Y G, Yang H. Improvements on decision method of grey target[J]. Systems Engineering and Electronics, 2011, 31(11):2634-2636.
[13]罗党.灰色多指标风险型决策方法研究[J].系统工程与电子技术,2004, 26(8):1057-1059.Luo D. Research on grey multi-criteria risk decision-making method[J]. Systems Engineering and Electronics,2004, 26(8):1057-1059.
[14]王大澳,菅利荣,刘思峰,等.基于Choquet积分的多属性灰靶群决策方法[J].控制与决策,2017, 32(7):1286-1292.Wang D A, Jian L R, Liu S F, et al. Approach for multi-attribute grey target group decision-making based on Choquet integral[J]. Control and Decision, 2017, 32(7):1286-1292.
[15]马金山.指标及权重均为混合数据类型的广义灰靶决策方法[J].统计与决策,2018(7):58-61.Ma J S. A generalized grey target decision method with mixed data type of index and weight[J]. Statistics and Decision, 2018(7):58-61.
[16]朱建军,张丽丽,梁艳华.基于冲突主体不确定证据融合的灰靶决策方法[J].控制与决策,2012, 27(7):1037-1041.Zhu J J, Zhang L L, Liang Y H. Grey target decision method based on uncertain evidence aggregation under conflict interest participants[J]. Control and Decision, 2012, 27(7):1037-1041.
[17]梁艳华.基于去键鼠的多时点多属性灰靶决策模型[J]·控制与决策,2012, 37(10):1527-1531.Liang Y H. Multi-perio and multi-criteria decision making model of grey target based on interval number[J].Control and Decision, 2012, 37(10):1527-1531.
[18]戴文战,李久亮.灰数多属性偏离靶心度群决策方法[J].系统工程理论与实践,2014, 34(3):787-792.Dai W Z, Li J L. Off-target deviation degree method grey multi-attribute group decision-making[J]. Systems Engineering—Theory&Practice, 2014, 34(3):787-792.
[19] Liu S F, Fang Z G, Yang Y J, et al. General grey numbers and their operations[J]. Grey Systems:Theory and Application, 2012, 2(3):341-349.
[20] Jiang S Q, Liu S F, Liu Z X, et al. Study on distance measuring and sorting method of general grey number[J].Grey System:Theory and Application, 2017, 6(3):319-328.